Problem: A circle has a radius of ${4}$. An arc in this circle has a central angle of $288^\circ$. What is the length of the arc? Either enter an exact answer in terms of $\pi$ or use $3.14$ for $\pi$ and enter your answer as a decimal. ${288^\circ}$ ${4}$
Solution: First, calculate the circumference of the circle. ${288^\circ}$ ${4}$ ${8\pi}$ ${c} = 2\pi r = 2\pi ({4}) = {8\pi}$ The ratio between the arc's central angle ${\theta}$ and $360^\circ$ is equal to the ratio between the arc length ${s}$ and the circle's circumference ${c}$. $\dfrac{{\theta}}{360^\circ} = \dfrac{{s}}{{c}}$ $\dfrac{{288}^\circ}{360^\circ} = \dfrac{{s}}{{{8\pi}}}$ $\dfrac{4}{5} = \dfrac{{s}}{{8\pi}}$ $\dfrac{4}{5} \times {8\pi} = {s}$ $\dfrac{32}{5}\pi = {s}$ ${288^\circ}$ ${4}$ ${8\pi}$ ${\dfrac{32}{5}\pi}$